To ensure the operation of the federal government after the Capitol was destroyed, President James Madison quickly appropriated for Congress the only public building that had escaped attack—the Patent and Post Office building, called Blodgett’s Hotel. Congress convened there from September 1814 until December 1815, when it moved to a temporary building where today’s Supreme Court stands.
The destruction of the Capitol by the Enemy having made it necessary that other accomodations [sic] should be provided for the meeting of Congress, chambers for the Senate and for the House of Representatives…have been fitted up…in the Public Building heretofore allotted for the Post and other Public Offices.
Records of the U.S. Senate, National Archives and Records Administration